MTH 162 Final: MTH 162 University of Rochester Fall 15Finalsol

• School: University of Rochester
• Department: Mathematics
• Course: MTH 162
• Professor: All

Document Summary

Part a: (15 points) evaluate the integral. Use the substitution x = 4 tan . Then dx = 4 sec2 d and. X2 + 16 = q16(tan2 + 1) = 16 sec2 = 4 sec . 16 z cos sin2 d = dx = z. 4 , by drawing a right triangle with one angle , we can check that sin = x. + c. so the answer becomes: (20 points) (a) compute the volume of a region bounded by the curves y = x3 + 1, y = 1 and x = 1 and rotated around the x-axis. Using the washer method we have radii of 1 and 1 + x3, so. 2 (b) set up the integral for the volume of the region bounded by y = x4, y = 0 and x = 2 and rotated around the x-axis. Using the washer method, the radius is x4, si.